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Blaszak M. — Multi-Hamiltonian Theory of Dynamical Systems
Blaszak M. — Multi-Hamiltonian Theory of Dynamical Systems

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Название: Multi-Hamiltonian Theory of Dynamical Systems

Автор: Blaszak M.

Аннотация:

This book offers a modern introduction to the Hamiltonian theory of dynamical systems, presenting a unified treatment of all types of dynamical systems, i.e., finite, lattice, and field. Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single coordinate system.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 350

Добавлена в каталог: 29.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Action variable      7
Adiabatic approximation      131
Adjoint action      254
Adjoint Lax eigenfunction      278
Adjoint mapping      253
Adjoint R-martix      259
Adjoint representatives      18
Adjoint symmetry      57
Adler map      284
AKNS, constrained isospectral problem      168
AKNS, Hamiltonian representation      292
AKNS, hierachy      279
AKNS, Lax hierarchy      95
AKNS, system      61
AKNS, zero courvature hierarchy      100
AKNS,(2+1)-dimensional      323 325
Algebra, dual      255
Algebra, exterior      30
Algebra, fundamental      111
Algebra, general      79
Algebra, Hamiltonian      80
Algebra, hereditary      73 105
Algebra, Lax isospectral      104
Algebra, Lie      42 43 45 46 252
Algebra, non-canonical action/angle      113
Algebra, noncanonical action/angle      79
Algebra, operator      327
Algebra, pseudo-differential operators      264 326
Algebra, shift operators      293
Algebra, Virasoro      73
Angle variable      7
Bargmann constraint      167
Basis      15
Benjamin — Ono equation      80
bi-Hamiltonian, chain      71 195
bi-Hamiltonian, systems      52 184 328
bi-Hamiltonian, vector field      49 242
Bi-vector      43
Boussinesq equation      272 286
Bracket, Lie      42 252 257
Bracket, Lie — Poisson      256
Bracket, Poisson      137
Bracket, Schouten      31
Burgers equation      272
Calogero — Moser system      245
Canonical, action/angle variables      7 110
Canonical, coordinates      5
Canonical, Poisson matrix      5
Canonical, representation      5
Casimir function      6 138 262
Characteristic operator equation      92
Closed k-form      28
Co-adjoint action      255
Compatible structures      65
Completely integrable      7
Conserved quantity      52
Constrained AKNS isospectral problem      168
Constrained DWW isospectral problem      167
Constrained MKdV isospectral problem      172
Constrained Schroedinger spectral problem      166
Constrained system      136
Constraint, Bargmann      167
Constraint, Kupershmidt      276
Contraction      15
Cosymmetry      57
Cotangent bundle      16
Covector fields      16
Davey — Stewardson equation      323
Derivative      18 21
Derivative, directional      23 27
Derivative, dual      19 21
Derivative, exterior      28 38
Derivative, Gateaux      91
Derivative, Lie      34 38
Derivative, total      25
Derivative, variational      81
Dirac reduction      263 284 287
Directional derivative      23 27
Dispersive water waves equation      50
Dressed operator      320
Dressing operator      319
Dual algebra      255
Dual derivative      19 21
Duality map      13 17 255
Dynamical system      1
Equation, AKNS      61
Equation, Benjamin — Ono      80
Equation, Boussinesq      272
Equation, Burgers      272
Equation, Calogero — Moser      245
Equation, cylindrical Korteweg-de Vries      62
Equation, Davey — Stewardson      323
Equation, dispersve water waves      50
Equation, Euler      6
Equation, field Gamier      236
Equation, Garnier      166 169
Equation, Hamilton — Jacobi      191 206
Equation, Harry-Dym      50
Equation, Henon — Heiles      4 143 185 200
Equation, Ishimori      324
Equation, Kadomtsev — Petviashvili      82 321 332
Equation, Kaup — Kupershmidt      276
Equation, KdV with sources      233
Equation, Kepler      215
Equation, Korteweg-de Vries      3 49 60 68 77 268
Equation, Melnikov      239
Equation, modified Boussinesq      273
Equation, modified dispersive water wave      84
Equation, modified Kadomtsev — Petviashvili      84 322
Equation, modified Korteweg-de Vries      49 61
Equation, modified Yang — Baxter      261
Equation, Neumann      167 220
Equation, Novikov — Veselov      333
Equation, relativistic Toda      311
Equation, Sawada — Kotera      61 277
Equation, Toda      3 62 243 295
Equation, Yang — Baxter      258
Euler equation      6
Evolution parameter      33
Exact k-form      28
Extended noninteracting particles      120
Extended phase space      138
Exterior derivative      28 38
Exterior product      30
Flow      2 32 54
Flow, constrained      166
Flow, isospectral      89
Flow, N-soliton      130
Flow, perturbed      131
Flow, restricted      177
Flow, stationary      137
Fundamental algebra      111
Garnier system      166 169
Gateaux derivative      91
Gelfand — Dikii spectral problem      283
General algebra      79
Gradient      23
Group Lie      250
Group of diffeomorphisms      32
Hamilton — Jacobi equation      191 206
Hamiltonian action/angle vector field      114
Hamiltonian algebra      80
Hamiltonian dynamical system      49
Hamiltonian formalism      5
Hamiltonian function      49
Hamiltonian vector field      49
Harry-Dym equation      50
Henon — Heiles system      143 185 200
Hereditary algebra      73 105
Hereditary operator      63
Hierarchy, elliptic separable potentials      208
Hierarchy, Harry-Dym-(2+1)      318
Hierarchy, Kadomtsev — Petviashvili      314
Hierarchy, matrix KP      322
Hierarchy, matrix modified KP      323
Hierarchy, modified Kadomtsev — Petviashvili      316
Hierarchy, Novikov — Veselov      332
Hierarchy, parabolic separable potentials      212
Hilbert transform      80
Implectic manifold      43
Implectic operator      43
Infinitesimal generator      32
Integral curve      1
Integrating factor      185
Interacting soliton      107
Interior product      27 38
Inverse Hamiltonian vector field      49
Inverse Pfaffian vector field      189
Ishimori equation      324
Isospectral deformation      2
Jacobi identity      18
Kadomtsev — Petviashvili equation      82 321 332
Kaup — Kupershmidt equation      276
KdV Lax hierarchy      94
Kepler problem      215
Kernel representation      335
Korteweg-de Vries equation      3 49 60 68 77 268
Kupershmidt constraint      276
Kupershmidt reduction      276
Lax, adjoint eigenfunction      278
Lax, dynamics      249
Lax, eigenfunction      278
Lax, hierarchies      266
Lax, isospectral equation      2
Lax, nonisospectral equation      91
Lax, operator      88
Lax, pair      2
Left action      252
Left invariant      251
Left translation      250
Legendre transformation      137
Leibniz rule      264
Levi-Civita condition      191
Lie, algebra      18 42 43 45 46 252
Lie, bracket      42 43 252 257
Lie, derivative      34 38
Lie, group      250
Lie, symmetry      55
Lie, transport      33
Linear system      109
Linear topological space      1
Manifold, bi-Poisson      64
Manifold, Poisson — Nijenhuis      65 241
Manifold, Riemannian      217
Master symmetries      78
Master tensor invariant      76
Melnikov system      239
Miura map      84
Modified Boussinesq equation      273 289
Modified dispersive water wave equation      84
Modified Gamier equation      175
Modified hierarchies      309
Modified Kadomtsev — Petviashvili equation      84 322
Modified KdV equation      49 61
Modified KdV with sources      235
Modified Yang — Baxter equation      261
multi-Hamiltonian vector fields      67
multi-vectors      30
Neumann equation      220
Neumann system      167
Newton representation      152
Newton stationary Harry-Dym      164
Newton stationary KdV      158
Nijenhuis, chain      195
Nijenhuis, coordinates      189
Nijenhuis, operator      63
Nijenhuis, torsion      64
Non-Hamiltonian symmetries      74 113
Nonisospectral problem      91
Nonisospectral zero-curvature equation      91
Nonlinear Schroedinger equation      50
Nonstandard Hamiltonian structure      220
Nonstandard Hamiltonian structure, DWW      229
Nonstandard Hamiltonian structure, field Gamier      236
Nonstandard Hamiltonian structure, KdV      224
Nonstandard Hamiltonian structure, Melnikov system      239
Novikov — Veselov equation      333
Operand      327
Operator, algebra      327
Operator, dressed      320
Operator, dressing      319
Operator, hereditary      63
Operator, implectic      43
Operator, Lax      88
Operator, Lax isospectral      101
Operator, Lax nonisospectral      101
Operator, normal form      138
Operator, Poisson      43
Operator, recursion      59
Operator, regular      138
Operator, symplectic      45
Operator, undressed      319
Operator, variational      24
Orbit      253
Ostrogradsky representation      137
Perturbed flow      131
Pfaffian vector field      189
Poincare lemma      28
Poisson bracket      43 137
Poisson manifold      43
Poisson operator      43
Poisson pencil      64
Pull-back      19
Push-forward      18
quasi-bi-Hamiltonian      185
R-matrix      249
R-structure      257
Reciprocal transformation      281
Recursion operator      59
Regular operator      138
Relativistic Toda lattice      311
Restricted flow      177
Restricted Harry-Dym      177
Restricted KdV      177 182
Riemannian manifold      217
Right action      252
Right invariant      251
Right translation      250
Sato equation      320
Sato theory      313
Sawada — Kotera equation      61 277
Scalar field      19
Schouten bracket      31
Separability      184
Separability elliptic potentials      208
Separability Garnier system      211
Separability Kepler equation      215
Separability spherically symmetric potentials      216
Separability stationary Harry-Dym      201
Separability stationary KdV      202
Separable system      191
Soliton, Hamiltonian vector fields      119
Soliton, particle      107 122
Soliton, perturbation theory      130
Soliton, solution      107
Staeckel space      218
Staeckel system      218
Stationary, DWW      141 145 149
Stationary, flow      137
Stationary, Harry-Dym      140 145 148
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